Looping Network Meetings

#51 April 29, 2024

Monday, 15:00 CET

Mathis Plapp

Phase-field models for interfacial pattern formation

Abstract:
The phase-field method describes moving interfaces and surfaces with the help of one or several scalar fields, the so-called phase fields. They can be interpreted physically as order parameters or mathematically as smoothed indicator functions. The equations of motion are obtained from the physics of phase transitions and the thermodynamics of irreversible processes. This results in nonlinear partial differential equations that can be numerically integrated with standard methods, without the need to explicitly track surfaces of complex geometry. The generality of the approach makes a large number of applications possible. In this talk, I will first give an introduction to the method, using as an elementary example the dendritic crystallization of a pure substance (see https://pmc.polytechnique.fr/~mp/Anims/dendlowanis.gif ). Then, I will discuss some extensions of the method and applications to grain growth and coarsening of grain-boundary networks in polycrystals and to viscous fingering in non-Newtonian fluids.

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